The water

Let L be the line parametrized by x = 2 + 2t, y = 3t, z = −1 − t. (a) Find a linear equation for the plane that is perpendicular

Elden [556K]

Answer:

Step-by-step explanation:

Given that L is a line parametrized by

$x = 2 + 2t, y = 3t, z = −1 − t$

The plane perpendicular to the line will have normal as this line and hence direction ratios of normal would be coefficient of t in x,y,z

i.e. (2,3,-1)

So equation of the plane would be of the form

$2x+3y-z =K$

Use the fact that the plane passes through (2,0,-1) and hence this point will satisfy this equation.

$2(2)+3(0)-(-1) =K\\K =5$

So equation is

$2x+3y-z =5$

b) Substitute general point of L in the plane to find the intersecting point

$2(2+2t)+3t-(-1-t) =5\\4+8t+1=5\\8t=0\\t=0\\(x,y,z) = (2,0,-1)$

i.e. same point given.

3 0

3 years ago

Store A

olga2289 [7]

Answer:

72

Step-by-step explanation:

3 0

3 years ago

The point R(-3,a,-1) is the midpoint of the line segment jointing the points P(1,2,b)

wlad13 [49]

Answer:

The values are:

$a = -5/2$

$b = -6$

$c = -7$

Step-by-step explanation:

Given:

P = (x₁, y₁, z₁) = (1, 2, b)

Q = (x₂, y₂, z₂) = (c, -7, 4)

m = R = (x, y, z) = (-3, a, -1)

To Determine:

a = ?

b = ?

c = ?

Determining the values of a, b, and c

Using the mid-point formula

$m\:=\:\left(\frac{x_1+x_2}{2},\:\frac{y_1+y_2}{2},\:\frac{z_1+z_2}{2}\right)$

As the point R(-3, a, -1) is the midpoint of the line segment jointing the points P(1,2,b) and Q(c,-7,4), so

m = R = (x, y, z) = (-3, a, -1)

Using the mid-point formula

$m\:=\:\left(\frac{x_1+x_2}{2},\:\frac{y_1+y_2}{2},\:\frac{z_1+z_2}{2}\right)$

given

(x₁, y₁, z₁) = (1, 2, b) = P

(x₂, y₂, z₂) = (c, -7, 4) = Q

m = (x, y, z) = (-3, a, -1) = R

substituting the value of (x₁, y₁, z₁) = (1, 2, b) = P, (x₂, y₂, z₂) = (c, -7, 4) = Q, and m = (x, y, z) = (-3, a, -1) = R in the mid-point formula

$m\:=\:\left(\frac{x_1+x_2}{2},\:\frac{y_1+y_2}{2},\:\frac{z_1+z_2}{2}\right)$

$\left(x,\:y,\:z\right)\:=\:\left(\frac{1+c}{2},\:\frac{2+\left(-7\right)}{2},\:\frac{b+4}{2}\right)$

as (x, y, z) = (-3, a, -1), so

$\left(-3,\:a,\:-1\right)\:=\:\left(\frac{1+c}{2},\:\frac{2+\left(-7\right)}{2},\:\frac{b+4}{2}\right)$

Determining 'c'

-3 = (1+c) / (2)

-3 × 2 = 1+c

$1+c = -6$

$c = -6 - 1$

$c = -7$

Determining 'a'

a = (2+(-7)) / 2

$2a = 2-7$

$2a = -5$

$a = -5/2$

Determining 'b'

-1 = (b+4) / 2

$-2 = b+4$

$b = -2-4$

$b = -6$

Therefore, the values are:

$a = -5/2$

$b = -6$

$c = -7$

6 0

3 years ago

The sun is 93,000,000 miles from Earth. What is the value of the 3 in the number 93,000,000

Lostsunrise [7]

Answer:

three million

Step-by-step explanation:

3 0

3 years ago

There was no more rainfall for the rest of the day.

Aleonysh [2.5K]

There’s no exact value listed on this graph, but it would be where the line ends completely on the far right. The rain was fluctuating throughout the day when the graph was going up and down. when the graph completely stops, the rain did too.

5 0

3 years ago